SFtraveler wrote:DS Problem - What is most efficient way to solve this DS problem? Please provide step-by-step solution.

If the ratio of integers a, b, and c is 1:2:3, what is the value of a+b+c?

1) c-a = 8

2) b-a = 4

Lets assume a=x, b = 2x, c = 3x
a+b+c = 6x = ? or x = ?

Statement 1:
c-a = 8 => 2x = 8
Sufficient

Statement 2 :
b-a = 4
=> x = 4
Sufficient

Hence D

solution of Anshu is ideal when one is familiar with ratio conversions and doesn't need to waste time on processing data.
another way to look at the problem would be
ac=1:2:3 => a/c=1/3, a/b=1/2, b/c=2/3 => solving the system of equations

a/c=1/3
c-a=8 => a=4, c=12

a/b=1/2
b-a=4 => a=4, b=8

after you went through the above solution, turn to the method of Anshu and have it sunk deeper, because it's useful and less time consuming

Thanks Anshu, that makes sense.

Night reader, thanks for your reply also. When you mention:

'solving the system of equations' then put a/c=1/3 and c-a=8 => a=4, c=12, I don't follow how a/c=1/3 turns into a=4 and c=12. Is that you just testing different sets of numbers in 1:3 ratio to get 4 and 12?

Same question for 4 and 8:
a/b=1/2
b-a=4 => a=4, b=8

SFtraveler wrote:Thanks Anshu, that makes sense.

Night reader, thanks for your reply also. When you mention:

'solving the system of equations' then put a/c=1/3 and c-a=8 => a=4, c=12, I don't follow how a/c=1/3 turns into a=4 and c=12. Is that you just testing different sets of numbers in 1:3 ratio to get 4 and 12?

Same question for 4 and 8:
a/b=1/2
b-a=4 => a=4, b=8

You are welcome !
a/c = 1/3 => c = 3a
c-a = 8 => 3a-a = 8 => a=4
c = 3a = 3*4 = 12

Similarly; a/b = 1/2 => b = 2a
b-a = 4 => 2a - a = 4
=> a =4
b = 2a = 2*4 = 8.

SFtraveler wrote:DS Problem - What is most efficient way to solve this DS problem? Please provide step-by-step solution.

If the ratio of positive integers a, b, and c is 1:2:3, what is the value of a+b+c?

1) c-a = 8

2) b-a = 4

The most efficient approach is to recognize that we don't have to solve; we need only determine whether there is sufficient information to solve.

Statement 1:
c-a = 8.
Since ac = 1:2:3, a/c = 1/3.
2 variables, 2 different linear equations. We can solve for a and c, then use the ratio of ac to solve for b.
Sufficient.

Statement 2:
b-a =4.
Since ac = 1:2:3, a/b = 1/2.
2 variables, 2 different linear equations. We can solve for a and b, then use the ratio of ac to solve for c.
Sufficient.

The correct answer is D.

We should do NO math for this problem. We should recognize that since each statement gives us a second linear equation, each is sufficient to solve for all 3 variables.